GATE 2020 ST – Question 29

Probability · Events and Conditional Probability · 1 mark · Numerical answer

Independent events E,F,G have probabilities1/2,1/3,1/4. If p is the probability that at least two occur, find12p (one decimal).

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Correct answer: 3.5 to 3.5

Explanation

Sum exactly-two and all-three events: p=(1/2)(1/3)(3/4)+(1/2)(1/4)(2/3)+(1/3)(1/4)(1/2)+(1/2)(1/3)(1/4)=7/24. Therefore12p=3.5. Independence permits multiplication of each event-and-complement combination.

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